Question

A satellite of mass m is in a circular orbit of radius r about the centre of the earth. A meteorite of the same mass, falling towards the earth, collides with the satellite completely inelastically. The speeds of the satellite and the meteorite are the same, just before the collision. The subsequent motion of the combined body will be

Answer 1

Answer: The resultant motion of the combined system will be such that it will start moving in an Elliptical motion.

Explanation:

Please refer to the attached diagram of before and after collision.

If the Velocity of the satellite is lesser than orbital velocity then satellite will fall down spirally on the earth's surface.

If the Velocity of satellite is same as the velocity of earth, then satellite moves in parabolic path.

If the Velocity of satellite is same as orbital velocity then satellite moves in a circular path.

If Velocity of satellite is more than earth's velocity then the satellite moves in a hyperbolic path.

It is given in that question that satellite initially moves in circular orbit.

Let the $v_o$ be the velocity of object after collision

Let $v_s$ be the velocity of satellite after collision

Applying law conservation of momentum,

m$v_s$ - m$v_o$   = 2 m$v_2$

∴ $v_2$ = $\frac{1}{2}$ X $\sqrt{2} v_o$ = $\frac{v_o}{2}$

∴ $v_2$ < $v_o$ < $\sqrt{\frac{GM}{R} }$

Hence, the combined resultant motion will be Elliptical motion.

Answer 2

Thus the motion of body will be in an elliptical orbit.

Explanation:

Given data:

• Mass of satellite = m
• Radius of circular orbit = r
• To find: Combined motion of body = ?

Solution:

Combined motion of the body = m v i + m v j

Motion = 2 mv^-1

v = 1 / √2 x √ GM / R

According to this derivation the motion of body will be in an elliptical orbit.